a railway half ticket costs half the full fare and the reservation charge is the same on half ticket as - Maths - Linear Equations in Two Variables

Question

a railway half ticket costs half the full fare and the
reservation charge is the same on half ticket as on full ticket one
reserved first class ticket from mumbai to ahmedabad costs Rs 216
and one full and one half reserved first class tickets cost Rs 327
what is the basic first class full fare and what is the reservation
charge

Vimala · Accepted Answer

Let x be the cost of full first class ticket from Mumbai to Ahmedabad.

Let y be the cost of reservation.

Since a reserved first class ticket costs Rs.216,

$x + y = 216$ ....(1)

Since one full and one half first class reserved ticket costs Rs.327,

$\frac{3}{2} x + 2 y = 327$ ....(2)

Thus, equations (1) and (2) form the system of equations.

Multiply equation (2) by 2 and rewrite the equation (2) as

$3 x + 4 y = 654$ ....(3)

Let us solve the system of equations (3) and (1).

$3 x + 4 y = 654$

$x + y = 216$

Multiply equation (1) by 3 to get

$3 x + 3 y = 648$ ....(4)

Subtract equation (4) from equation (3) to get

$3 x + 4 y - 3 x - 3 y = 654 - 648 4 y - 3 y = 6 y = 6$

Substitute the value of y in equation (1) to get the value of x

$x = 216 - 6 = 210$

Thus, the first class ticket from Mumbai to Ahmedabad is Rs.210 and the reservation cost is Rs.6